The complete answer to your question is pretty long, but I’ll try to summarize. Before the U.S. was a country, and even for a while afterward, the primary currency was the "Spanish milled dollar", also called a "piece of eight". It got the "dollar" name from an adaptation of the Spanish name for the coin, "Juachim’s Thaler", or juachimsthaler, or thaler, and eventually dollar. The quarter is simply one-fourth of a dollar, thus a quarter dollar, or quarter. The nickel gets its name from its metallic content. The dime was originally spelled "disme" (but still pronounced "dime") from the French, but the U.S. mint anglicized the word to "dime" after a few years.